∫(secx)^3 dx
=∫secx dtanx
=secx.tanx -∫secx.(tanx)^2 dx
=secx.tanx -∫secx.[(secx)^2 -1] dx
2∫(secx)^3 dx =secx.tanx +∫ secx dx
∫(secx)^3 dx =(1/2)[secx.tanx +ln|secx+tanx|] + C
//
∫(secx)^5 dx
=∫ (secx)^3 dtanx
=(secx)^3.tanx - 3∫ (secx)^3.(tanx)^2 dx
=(secx)^3.tanx - 3∫ (secx)^3.[(secx)^2 -1] dx
4∫(secx)^5 dx =(secx)^3.tanx + 3∫ (secx)^3 dx
∫(secx)^5 dx
=(1/4)(secx)^3.tanx + (3/4)∫(secx)^3 dx
=(1/4)(secx)^3.tanx + (3/8)[secx.tanx +ln|secx+tanx|] + C
=∫secx dtanx
=secx.tanx -∫secx.(tanx)^2 dx
=secx.tanx -∫secx.[(secx)^2 -1] dx
2∫(secx)^3 dx =secx.tanx +∫ secx dx
∫(secx)^3 dx =(1/2)[secx.tanx +ln|secx+tanx|] + C
//
∫(secx)^5 dx
=∫ (secx)^3 dtanx
=(secx)^3.tanx - 3∫ (secx)^3.(tanx)^2 dx
=(secx)^3.tanx - 3∫ (secx)^3.[(secx)^2 -1] dx
4∫(secx)^5 dx =(secx)^3.tanx + 3∫ (secx)^3 dx
∫(secx)^5 dx
=(1/4)(secx)^3.tanx + (3/4)∫(secx)^3 dx
=(1/4)(secx)^3.tanx + (3/8)[secx.tanx +ln|secx+tanx|] + C